Let the domain for x be the set of all students in this class and the domain for y be theset of all countries in the world. Let P(x, y) denote student x has visited country y andQ(x, y) denote student x has a friend in country y. Express each of the following usinglogical operations and quantifiers, and the propositional functions P(x, y) and Q(x, y).

(a) Carlos has visited Bulgaria.

(b) Every student in this class has visited the United States.

(c) Every student in this class has visited some country in the world.

(d) There is no country that every student in this class has visited.

(e) There are two students in this class, who between them, have a friend in every countryin the world.

(f) Nobody in this class has visited a country in which they did not have a friend